Yi-Hong Wu

Sharp detection thresholds for random geometric graphs with polynomial average degrees

We study the random geometric graph formed by connecting $n$ independent uniform points on $\mathbb S^{d-1}$ whenever their inner product exceeds a threshold chosen to give edge density $p$. We establish the conjectured dimensionality threshold for indistinguishability from the Erd\"{o}s-R\'enyi graph $G(n,p)$ througho...